JezK
Edit File: mkpic
#!/usr/bin/perl # Debian required shebang above # Original shebang below # #!/usr/bin/env perl use constant Version => '1.02'; my $help = <<'DOC' = mkpic - interface for making pictures with mfpic = Synopsis mkpic [options] [picfile] Options: -c,--clean remove all but the input file and die -p,--pdfsample create pdf file with sample images -f,--font=<font command> set default font for labels --[no]box produce framed boxes -V,--version report version number and die -h,--help display help info and die --[no]debug display debugging information -l,--log=<logfile> file for warning messages Without an input file, the DATA section is used. = Command overview begin name xl yl xmin ymin xmax ymax xlabel ylabel end stop var=value # comment arccst xcenter ycenter xstart ystart theta arcset xstart ystart xend yend theta arccrtt xcenter ycenter radius theta1 theta2 arc3 x1 y1 x2 y2 x3 y3 xmark [label1] x1 [label2] x2 ... Xmark [label1] x1 [label2] x2 ... ymark [label1] y1 [label2] y2 ... Ymark [label1] y1 [label2] y2 ... xdrop x y ydrop x y xydrop x y arrow x1 y1 x2 y2 label label YX x y label xlabels YX x y dx label ... ylabels YX x y dy label ... point x1 y1 x2 y2 ... dpoint x1 y1 dx1 dy1 ... lines x1 y1 x2 y2 ... dlines x1 y1 dx1 dy1 ... curve x1 y1 x2 y2 ... dcurve x1 y1 dx1 dy1 ... rect x1 y1 x2 y2 drect x y dx dy dcrect x y dx dy crect x1 y1 x2 y2 arect xc yc width height theta bar x xdev height func xmin xmax step expression-in-x grid dx dy xgap ygap hatch bhat ehat = Description mkpic provides an easy interface for making small pictures with mfpic. To this end you create an input file has to be created consisting of commands, one per line, with space separated parameters (or you modify the DATA section of the mkpic script, which is used if you run it without an input file). For an extensive description see the file mkpicdoc.pdf, which is part of the distribution. mkpic produces two files. Assuming an input file named |picfile| defaulting to |mkpic| these are: picfile.mac a macro file which will contain |TeX| commands for every picture picfile.sty a style file for latex, defining the same |TeX| commands for every picture. With the |--pdfsample| option, two other files are produced: picfile.pdf a PDF file containing all pictures. This lets you easily check the results of your designs. picfile.tex the |TeX| source used for creating this PDF file. In |LaTeX|, you have to include |\usepackage{picfile}| and to include commands like |\Fig|/name/ in your source, where /name/ is the name you gave one of your pictures in an mkpic |begin| command. In TeX and ConTeXt, you have to |\input picfile.mac| and to include commands like |\Fig|/name/ in your source, where /name/ is the name you gave one of your pictures in an mkpic |begin| command. In TeX, you must use the |\bye| command (/not/ |\end| to finish your TeX source See the RUNNING section for how to run mkpic and TeX, LaTeX, or ConTeXt. = Commands The source is set up so that it is easy to add your own commands, Currently the following commands have been implemented (the arguments are not listed here; for those, refer to the SYNOPSIS section): begin, end Every picture begins with the |begin| command and ends with the |end| command. The |begin| command defines a name for the picture and defines a tex command with that name, prefixed with 'Fig'. The resulting command is written to a |.mac| file. Thus the command begin aa ... starts writing |\def\Figaa{...| to the |.mac| file, and the picture can be reproduced in a |TeX| document by importing the |.mac| file and using the |\Figaa| command. xl and yl are the lengths of the x- and y-axes. xlabel and ylabel are the label that are placed at the ends of those axes. Use a space to suppress labeling, or "-" to suppress drawing the axes at all. stop stops further reading of the input. Useful if you have many pictures, but want to see only the first few for testing purposes. var=value sets the variable var to value. This variable, or an expression containing it, can be used instead of any numerical parameter. Variable names may contain lower and uppercase letters, digits or underscores, with the restriction that they must start with a letter and may not end in an underscore. # denotes a comment xmark, ymark, Xmark, Ymark These commands place one or more labels along the x- or y-axes, either below (|xmark| and |ymark|) or above (|Xmark| and |Ymark|) the axis. For the |[xXyY]mark| commands a parameter containing any character other than [-.0-9] is interpreted as the label (this implies that you cannot use expressions here!) to be placed and its position is expected in the next parameter. If a parameter is just a number, it is placed at that x-position. If you want a number to be interpreted as a label, put it in braces: |{1950}|. arccst (Mnemonic: |c|enter |s|tart |t|heta.) Draws an arc with its center in |xcenter,ycenter|, starting in |xstart,ystart| and with an arc length of |theta| degrees. arcset (Mnemonic: |s|tart |e|nd |t|heta.) Draws an arc starting in |xstart,ystart|end ending in |xend,yend| and with an arc length of |theta| degrees. arccrtt (Mnemonic: |c|enter |r|adius |t|heta1 |t|heta2.) Draws an arc with its center in |xcenter,ycenter|, a radius |radius| starting at |theta1| degrees and ending at |theta2| degrees. arc3 (Mnemonic: |3| points.) Draws an arc starting at |(x1,y1)|, through |(x2,y2)| and ending in |(x3,y3)|. xdrop, ydrop, xydrop These commands draw dotted arrows perpendicularly to the x-axis, the y-axis and both axes, respectively, ending on the axes with the arrow head. arrow draws an arrow from |(x1,y1)| to |(x2,y2)| labeled on its tail with |label| label draws a label at |(x,y)|. |YX| tells how it will be adjusted: for Y=t,b,c |(x,y)| will be, in the y-direction, on top, bottom or center of the label respectively, for X=l,r,c it will be, in the x-direction, left, right or center adjusted on |(x,y)|. Thus label tl 0 0 Hello World! will draw the string "Hello World" with its lower left corner at (0,0) xlabels draws many labels, starting at |(x,y)|, and incrementing |x| with |dx| after every label. |YX|: see |label|. Labels may not contain spaces; if you need spaces, use - instead. ylabels Same as |xlabels|, but incrementing |y| with |dy| instead. point draws points (dots) at |(x1,y1)|, |(x2,y2)| et cetera. dpoint draws points (dots) starting at |(x1,y1)| and then moving by |(dx1,dy1)|, |(dx2,dy2)| et cetera. lines draws line segments from |(x1,y1)| to |(x2,y2)|, |(x3,y3)| et cetera. dlines draws line segments starting at |(x1,y1)| and then moving by |(dx1,dy1)|, |(dx2,dy2)| et cetera. curve draws a bezier curve from |(x1,y1)| to |(x2,y2)|, |(x3,y3)| et cetera. dcurve draws a bezier curve starting at |(x1,y1)| and then moving by |(dx1,dy1)|, |(dx2,dy2)| et cetera. rect draws a rectangle with diagonal points at |(x1,y1)| and |(x2,y2)|. drect draws a rectangle with diagonal points at |(x,y)| and |(x+dx,y+dy)|. crect clears a rectangle with diagonal points at |(x1,y1)| and |(x2,y2)|. dcrect clears a rectangle with diagonal points at |(x,y)| and |(x+dx,y+dy)|. arect draws a rectangle with a widdh |width| and a height |height|; the middle of the bottom is at |(xc,yc)| and the centerline through |(xc,yc)| makes an angle |theta| with the x-axis. bar draws a equivalent with |rect x-xdev 0 x+xdev height| func draws the function given by |expression-in-x| between |xmin| and |xmax|, stepping with |step| units in the x-direction. Note that the |expression-in-x| will be evaluated by |Metafont|, so you will have to use metafont syntax. grid draw dotted grid lines at distances dx and dy in the x- and y directions; the gaps between the dots are set to |xgap| an |ygap| respectively. For an esthetic appearance, be sure to use integer |dx/xgap| and |dy/ygap| ratios. hatch hatch the closed curve that follows. bhat starts a path that will eventually be closed, and then hatched. ehat ends a path started with |bhat|, closes it and then hatches it. anything else will be inserted as is in the macro file, and therefore should be a valid |mfpic| statement. You use this when you need such a statement only once, or a few times and therefore see no need to define a proper command for it. = Running mkpic/TeX The effect of running mkpic picfile is the creation of |picfile.mac|, which you can |\input| into a TeX or ConTeXt source, and |picfile.sty| which can be input into a LaTeX source using the |\usepackage| command. After running TeX (or LaTeX or ConTeXt), you will find a file |picfile.mf| and you will have to run Metafont on it, which (assuming you configured TeX for 600 dpi) produces picfile.600gf. This file will have to be converted to a pk file with gftopk. Finally, you need to run TeX, normally at least twice, again. So for pdfLaTeX the sequence is: mkpic picfile pdflatex file.tex mf picfile gftopk picfile.600gf pdflatex file pdflatex file = Bug Currently only up to 256 pictures can be generated. In the future this problem will probably be solved by introducing more than one font and generating tex-command names that have the font name in front. = Changes Changes with respect to version 0.1: - added mkpicdoc.tex to the distribution = Author and copyright Author Wybo Dekker Email U{Wybo@dekkerdocumenten.nl}{wybo@dekkerdocumenten.nl} License Released under the U{www.gnu.org/copyleft/gpl.html}{GNU General Public License} DOC ; use vars qw/$xgap $ygap $dx $dy $xl $yl $x3 $y3 $height $Z $d $F $r $theta1 $theta2/; sub evaluate { defined or die "Missing parameter at line $.\n"; if ( !m|^[0-9.]+$| ) { my $x = ''; # we build up the expression with $-ized variable names in $x while ($_) { unless (/[A-Za-z0-9]+/) { $x .= $_; last } my ( $left, $middle, $right ) = ( $`, $&, $' ); $x .= $left . ( ( $middle =~ m|^[0-9.]+$| || $fun{$middle} ) ? "" : '$' ) . $middle; $_ = $right; } $_ = $x; eval "\$_=$_" while m|[^0-9.-]|; } $_; } sub parse { my @x; ( $command_name, @x ) = split ( /\s+/, $_, scalar @_ + 1 ); # input values/expressions in @x print LOG "command: $command_name\n" if $debug; for ( my $i = 0 ; $i < @_ ; $i++ ) { # each variable to be set $_ = $x[$i]; # take the expression if ( $_[$i] !~ /^[A-Z]/ ) { # if name of receiving var not capitalized: await numerical evaluate; } my $varname = "$_[$i]"; $$varname = $_; print LOG "$varname=$_\n" if $debug; } } sub parse_array { my @x; ( $command_name, @x ) = split ( /\s+/, $_[0] ); print LOG "command: $command_name\n" if $debug; unless ( $command_name =~ /mark/ ) { for (@x) { evaluate; } } print LOG "parse_array returns: @x\n" if $debug; @x; } sub open_macrofile { my $rerun = 0; # we need to rerun if: # - one of the needed files is missing or else # - the input file is newer than the .mac file or else # - the present options differ from/keep the previous ones # check the presence of needed files: chomp( $_ = -f $tex ? $tex : `which mkpic` ); my $inputtime = ( stat($_) )[9]; for ( "mac", "sty" ) { -f "$tex.$_" or $rerun = 1, last; } # if all are there, test if the input is older than the .mac file: !$rerun && ( stat("$tex.mac") )[9] > $inputtime or $rerun = 1; # if that's true too, check that the previous option were the same: unless ($rerun) { open( MAC, "$tex.mac" ); $_ = <MAC>; $_ eq $options or $rerun = 1; close MAC; } $rerun or return (0); open( MAC, ">$tex.mac" ); select MAC; $_ = <<'EOF' % vim: syntax=tex \input mfpic \let\circle\undefinedcs \mfpicunit.01mm \opengraphsfile{TX} \def\ifundefined#1{\expandafter\ifx\csname#1\endcsname\relax} \def\doatend{\closegraphsfile} \ifundefined{typefile}\else\appendtoks\doatend\to\everystoptext\fi % for context \ifundefined{documentclass}\else\AtEndDocument{\doatend}\fi % for latex \def\bye{\doatend\par\vfill\supereject\end} % plain \def\ruledhbox#1{\vbox{\hrule\hbox{\vrule\kern3pt \vbox{\kern3pt#1\kern3pt}\kern3pt\vrule}\hrule}} EOF ; s/^\s+//gm; s/TX/$tex/gm; print MAC $options,$_; open( STY, ">$tex.sty" ) or die "Could not open $tex.sty: $!\n"; $_ = <<'EOF' \ProvidesPackage{TX} \input TX.mac \endinput EOF ; s/^\s+//gm; s/TX/$tex/gm; print STY; 1; } sub sys { system("@_") and die "@_: $?\n"; } sub parse_input { while (<$input>) { chomp; s/\s*#.*//; # remove comment next unless $_; # skip empty lines /^begin/ and do { parse qw(Name xl yl xmin ymin xmax ymax Xlabel Ylabel); $names{$Name} and die "multiple occurrences of picture named $Name\n"; $names{$Name} = 1; $Xlabel = "" if $Xlabel eq '-'; $Ylabel = "" if $Ylabel eq '-'; $xscale = int( 100 * $xl / ( $xmax - $xmin ) + .5 ); $yscale = int( 100 * $yl / ( $ymax - $ymin ) + .5 ); $sx = sprintf( "%.2f", 100 / $xscale ); $sy = sprintf( "%.2f", 100 / $yscale ); $yx = $ymin > 0 ? $ymin : 0; # y-position of the x-axis $xy = $xmin > 0 ? $xmin : 0; # x-position of the y-axis $xlo = $xy - $sx; # x-pos of right side of y-markers $ylo = $yx - $sy; # y-pos of top side of x-markers $xhi = $xmax + 3 * $sx; # x-pos of left side of x-labels $yhi = $ymax + 3 * $sy; # y-pos of bottom side of y-labels print "%\n%====$Name====\n" . "\\def\\Fig$Name\{\\$box\{\\mftitle{$Name}%\n" . "\\def\\xlo{$xlo}\\def\\xhi{$xhi}%\n" . "\\def\\ylo{$ylo}\\def\\yhi{$yhi}%\n" . "\\def\\xy{$xy}\\def\\yx{$yx}%\n" . "\\mfpic[$xscale][$yscale]{$xmin}{$xmax}{$ymin}{$ymax}%\n" . "\\hatchwd{2}%\n" . ( $Xlabel ? "\\tlabel[bc]($xy,$yhi){$font $Ylabel}%\n" : '' ) . ( $Ylabel ? "\\tlabel[cl]($xhi,$yx){$font $Xlabel}%\n" : '' ); print TEX "\\Fig$Name\\par{\\bf $Name}\\eject\n" if $pdfsample; }, next; /^arccst/ and do { # arc center start theta parse qw(xc yc x1 y1 theta); print "\\arc[c]{($xc,$yc),($x1,$y1),$theta}\n"; }, next; /^arcset/ and do { # arc start end theta parse qw(x1 y1 x2 y2 theta); print "\\arc[s]{($x1,$y1),($x2,$y2),$theta}\n"; }, next; /^arccrtt/ and do { # arc center radius theta1 theta2 parse qw(xc yc r theta1 theta2); print "\\arc[p]{($xc,$yc),$theta1,$theta2,$r}\n"; }, next; /^arc3/ and do { # arc three points parse qw(x1 y1 x2 y2 x3 y3); print "\\arc[t]{($x1,$y1),($x2,$y2),($x3,$y3)}\n"; }, next; /^arrow/ and do { parse qw(x1 y1 x2 y2 Label); my $yd = $y1 > $y2 ? -3 : 3; print "\\tlabel[bc]($x1,$y1){$font $Label}%\n" . "\\arrow\\lines{($x1," . ( $y1 + $yd * $sy ) . "),($x2,$y2)}%\n"; }, next; /^[xyXY]mark/ and do { @z = parse_array($_); for ( $i = 0 ; $i < @z ; $i++ ) { $label = $z[$i]; if ( $label =~ /^[-.\d]+$/ ) { $label = "\$$label\$"; } else { $i++; } $x = $command_name =~ /x/i ? $z[$i] : $command_name =~ /y/ ? $xlo : -$xlo; $y = $command_name =~ /y/i ? $z[$i] : $command_name =~ /x/ ? $ylo : -$ylo; print "\\tlabel[$pos{$command_name}]($x,$y)" . "{\\rm \\strut $label}%\n"; } }, next; /^grid/ and do { parse qw(xdist ydist xgap ygap); $topmaxy = ( int( $ymax / $ydist ) * $ydist ); $lftmaxx = ( int( $xmin / $xdist ) * $xdist ); $botmaxy = ( int( $ymin / $ydist ) * $ydist ); $rtmaxx = ( int( $xmax / $xdist ) * $xdist ); for ( $t = $lftmaxx ; $t <= $rtmaxx ; $t += $xdist ) { print "\\dotted[.5pt,$xgap mm]\\lines{($t,$botmaxy),($t,$topmaxy)}%\n"; } for ( $t = $botmaxy ; $t <= $topmaxy ; $t += $ydist ) { print "\\dotted[.5pt,$ygap mm]\\lines{($lftmaxx,$t),($rtmaxx,$t)}%\n"; } }, next; /^bar/ and do { parse qw(x xdev height); $x1 = $x - $xdev; $x2 = $x + $xdev; $y1 = 0; $y2 = $height; print "\\rect{($x1,$y1),($x2,$y2)}%\n"; }, next; /^d?(point|lines|curve|rect|crect)/ and do { @z = parse_array($_); $command_name =~ /^d/ and do { # relative points for ( $i = 3 ; $i < @z ; $i += 2 ) { $z[$i] += $z[ $i - 2 ]; $z[ $i - 1 ] += $z[ $i - 3 ]; } $command_name =~ s/^d//; }; $_ = "$command_name @z"; # for example: crect 5 20 20 5 s/^/\\/; # \crect 5 20 20 5 s/\s+/{(/; # \crect{(5 20 20 5 while (/ +/) { s/ +([-.\d]+)(\s+)?/,$1),\n(/; } # \crect{(5,20),(20,5) s/,\n\($/}/; # \crect{(5,20),(20,5)} s/crect/gclear\\rect/; # \gclear\rect{(5,20),(20,5)} print "$_\n"; }, next; /^func/ and do { parse qw(x y d F); print "\\function{$x,$y,$d}{$F}%\n"; }, next; /^hatch/ and do { print '\rhatch\draw\lclosed'; }, next; /^bhat/ and do { print '\rhatch\lclosed\connect', "\n"; }, next; /^ehat/ and do { print '\endconnect', "\n"; }, next; /^xdrop/ and do { parse qw(x y); print "\\dotted\\arrow" . "\\lines{($x,$y),($xy,$y)}%\n"; }, next; /^ydrop/ and do { parse qw(x y); print "\\dotted\\arrow" . "\\lines{($x,$y),($x,$yx)}%\n"; }, next; /^xydrop/ and do { parse qw(x y); print "\\dashed\\arrow" . "\\lines{($x,$y),($xy,$y)}%\n"; print "\\dashed\\arrow" . "\\lines{($x,$y),($x,$yx)}%\n"; }, next; /^xlabels/ and do { parse qw(M x y dx Z); @z = split ( /\s+/, $Z ); for (@z) { print "\\tlabel[$M]($x,$y){$font $_}%\n"; $x += $dx; } }, next; /^ylabels/ and do { parse qw(M x y dy Z); @z = split ( /\s+/, $Z ); for (@z) { print "\\tlabel[$M]($x,$y){$font $_}%\n"; $y += $dy; } }, next; /^label/ and do { parse qw(M x y Label); $M =~ /^[bct][lcr]$/ or die "illegal label in $_\n"; print "\\tlabel[$M]($x,$y){$font $Label}%\n"; }, next; /^end/ and do { # axes drawn last for easier rect clears: print "\\arrow[\\axisheadlen]\\lines" . "{($xmin,$yx),($xmax,$yx)}%\n" if $Xlabel; print "\\arrow[\\axisheadlen]\\lines" . "{($xy,$ymin),($xy,$ymax)}%\n" if $Ylabel; print "\\endmfpic}}%\n"; }, next; /^arect/ and do { parse qw/xc yc w h theta/; $theta *= 3.141592 / 180; $ws = $w / 2 * sin($theta); $wc = $w / 2 * cos($theta); $hs = $h * sin($theta); $hc = $h * cos($theta); print "\\lines{($xc-$ws,$yc+$wc),($xc-$ws+$hc,$yc+$wc+$hs),($xc+$ws+$hc,$yc-$wc+$hs),($xc+$ws,$yc-$wc),($xc-$ws,$yc+$wc)}\n"; }, next; /^(\w+)\s*=/ and do { $var = $1; evaluate; print LOG "$var=$$var\n" if $debug; }, next; /^stop/ and do { last }; # stop reading the input print "$_\n" if $_; # anything else printed literally } print MAC "\\endinput\n"; close(MAC); if ($pdfsample) { print TEX "\\bye\n"; close(TEX); sys("pdftex --interaction batchmode $tex 2>/dev/null"); sys("mf $tex; gftopk $tex.${dpi}gf"); sys("pdftex --interaction batchmode $tex 2>/dev/null"); for ( ( "log", "mf", "tfm", "${dpi}pk", "${dpi}gf", ) ) { unlink "$tex.$_"; } } } sub help { undef $/; open(FH,$0); print "Usage:".[split(/= .*\n/,<FH>)]->[3]; exit 1 } sub install { system('instscript --extras=mkpicdoc.tex,mkpicdoc.pdf -zp mkpic'); exit 0; } use Getopt::Long; Getopt::Long::Configure("bundling_override"); GetOptions( 'c|clean' => \$clean, # remove all but input file and don't run 'p|pdfsample' => \$pdfsample, # create pdf file with sample images 'b|box!' => \$box, # produce framed boxes 'f|font=s' => \$font, # default font instead of rm 'V|version' => \$version, # report version number and die 'h|help' => \&help, # display help info and die 'd|debug!' => \$debug, # print debug information 'l|log=s' => \$log, # file for warning messages 'I' => \&install # not for general use ); if ($version) { print Version."\n"; exit; }; $font = $font || '\rm'; $box ||= ''; $pdfsample ||= 0; if ($log) { open( LOG, ">>$log" ) or die "Could not open $log for output: $!\n"; } else { *LOG = *STDERR; } # find printer density if ( open( IN, `kpsewhich --format="web2c files" mktex.cnf` ) ) { while (<IN>) { /BDPI=(\d+)/ and $dpi = $1, last; } } else { print LOG "could not find mktex.cnf; forcing 600dpi\n"; $dpi = 600; } # we'll place the options in the .mac file so that, in the next run, # we can see if the previous run had the same options; if so and if # the input file is older than the .mac file, we won't rerun mkpic: $options = "% font:$font box:$box dpi=$dpi pdfsample:$pdfsample\n"; $tex = shift; if ($tex) { open( IN, $tex ) or die "Could not open $tex\n"; $input = *IN; } else { $input = *DATA; $tex = 'mkpic'; } $clean and do { for ( eval "qw(mf ${dpi}gf ${dpi}pk log dvi pdf mac tex tfm sty)" ) { unlink "$tex.$_"; } exit 0; }; open_macrofile() or die "mkpic: no new run needed\n"; print LOG "Mkpic Warning: Rerun (La)TeX\n" if $log; $box = $box ? 'ruledhbox' : 'hbox'; if ($pdfsample) { open( TEX, ">$tex.tex" ); ($_ = <<EOF ) =~ s/^\s+//gm; \\input $tex.mac \\parindent0pt\\parskip2ex \\nopagenumbers\\vsize=260mm EOF print TEX; } %pos = ( 'xmark' => 'tc', # positions for [xyXY]marks 'ymark' => 'cr', 'Xmark' => 'bc', 'Ymark' => 'cl' ); %fun = ( sin => 1, cos => 1, sqrt => 1, atan2 => 1, abs => 1, exp => 1, int => 1, log => 1, not => 1 ); %names = (); parse_input; __DATA__ l=20 begin steps l l 0 0 l l - - \pen{2pt} dlines 10 10 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 end begin rectangle 64 64 0 0 10 10 $x$ $y$ arect 5 5 3 2 60 lines 0 0 10 10 0 10 10 0 end begin parabola 64 64 0 -6 4 5 $x$ $y$ xmark 2 Xmark 3 ymark -5 0 4 bhat lines 0 0 0 4 func 0 3 .05 4-x*x lines 3 -5 3 0 ehat func 0 3.2 .05 4-x*x xydrop 3 -5 arrow 3 4 1.7 1.1 $f(x)=4-x^2$ arrow 2 5 1 2 Area $O_1$ arrow 4 2 2.8 -2 Area $O_2$ end begin droparrows 64 64 0 3 12 8 $x$ $y$ xmark $a$ 2 $x_1$ 4 $x_2$ 8 $b$ 10 ydrop 2 4.414 ydrop 4 5 ydrop 8 5.828 ydrop 10 6.162 label cc 4 4 $f(x_1)$ label cc 8 4 $f(x_2)$ label cc 7 8 $f(x)$ increasing on $[a,b]$ label cc 7 7.5 $x_1<x_2\Rightarrow f(x_1)<F(x_2)$ func 1 11 .1 x**(.5)+3 end begin asymptotes 64 64 0 0 10 10 $x$ $y$ curve 1 1 2 3 4 5.7 7 8.1 9 9 point 2 3 4 5.7 7 8.1 \shift{(-.05,.05)} func 1.4 2.6 .1 1.65*x-.3 func 3.2 4.8 .1 1.025*x+1.6 func 6.1 7.9 .1 .62*x+3.76 label cl 9.5 9 $f(x)$ label tl 5 5 $f^\prime(x)>0$ label tl 5 4 $f^\prime(x)$ decreasing end # the previous diagram was made when expression were not yet available # with them, it's easier to use a defined curve and its calculated slopes # and positions: begin droppers 64 64 0 0 10 10 $x$ $y$ func 0 10 .1 3*(sqrt(x)) point 2 3*sqrt(2) 4 3*sqrt(4) 7 3*sqrt(7) \shift{(-.05,.05)} func 1.5 2.5 .1 3/2*(x/sqrt(2)+sqrt(2)) func 3.5 4.5 .1 3/2*(x/sqrt(4)+sqrt(4)) func 6.5 7.5 .1 3/2*(x/sqrt(7)+sqrt(7)) label cl 9.5 9 $f(x)$ label tl 5 5 $f^\prime(x)>0$ label tl 5 4 $f^\prime(x)$ decreasing end begin inflections 64 64 -.85 -1.5 1.5 5 $x$ $y$ func -.6 1.5 .05 6*(x**4)-8*(x**3)+1 lines -.2 1 .2 1 label cr -.25 1 horizontal arrow .5 2 0 1 inflection point arrow .8 1 .65 0 inflection point arrow 1 5 1.5 4.375 $f(x)=6x^4-8x^3+1$ Xmark 1 ymark \raise-8pt\hbox{0} 0 -1 xydrop 1 -1 end begin paraboloid 64 64 -4 -4 4 4 - - \dashed lines -4 0 0 0 0 0 0 -4 # neg z and neg y \dashed lines 0 0 3 1.73 # neg x \arrow lines 0 0 0 4 # pos z \arrow lines 0 0 4 0 # pos y \arrow lines 0 0 -3 -1.73 # pos x \dotted lines -1 4 -1 0 -4 -1.73 # intersections y=-1 plane \dotted lines -1 -.577 -4 -.577 # intersection x=2 plane with xy-plane % extra helplines \dotted lines -2 .423 -2 -.577 0 0 0 1 -2 .423 Ymark 3 % end of extras \dotted lines 0 3 -1 3 -4 1.27 \dashed\sclosed curve -3 2.42 -1.5 2.711 -1 2.42 -2.5 2.134 label bc 0 yhi $z$ label cl xhi 0 $y$ label tr -3.1 -1.8 $x$ label cl -.85 -.577 2 label tc 0 5.5 $f(x,y)=x^2-4x+2y^2+4y+7$ xmark -1 Ymark 1 \shift{(-2,.42)} \dashed func 0 .5 .1 9*x*x func -.5 0 .1 7*x*x \dashed func -1 0 .1 2*x*x func 0 1 .1 2*x*x end